Abstract
Set-membership (SM) adaptive filtering is appealing in many practical situations, particularly those with inherent power and computational constraints. The main feature of the SM algorithms is their data-selective coefficient update leading to lower computational complexity and power consumption. The set-membership affine projection (SM-AP) algorithm does not trade convergence speed with misadjustment and computation complexity as many existing adaptive filtering algorithms. In this work analytical results related to the SM-AP algorithm are presented for the first time, providing tools to setup its parameters as well as some interpretation to its desirable features. The analysis results in expressions for the excess mean square error (MSE) in stationary environments and the transient behavior of the learning curves. Simulation results confirm the accuracy of the analysis and the good features of the SM-AP algorithms.
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The author would like to thank the financial support provided by CNPq and FAPERJ, national and state research councils, respectively. He also wants to thank Markus V.S. Lima for carefully reading the manuscript and for checking the simulations.
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Diniz, P.S.R. Convergence Performance of the Simplified Set-Membership Affine Projection Algorithm. Circuits Syst Signal Process 30, 439–462 (2011). https://doi.org/10.1007/s00034-010-9219-z
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DOI: https://doi.org/10.1007/s00034-010-9219-z